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Random Symmetrizations of Convex Bodies

Published online by Cambridge University Press:  22 February 2016

D. Coupier*
Affiliation:
Université Lille 1
Yu. Davydov*
Affiliation:
Université Lille 1
*
Postal address: Laboratoire Paul Painlevé, UMR CNRS 8524, Université Lille 1, 59 655 Villeneuve d'Ascq Cédex, France.
∗∗ Email address: david.coupier@math.univ-lille1.fr
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Abstract

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In this paper we investigate the asymptotic behavior of sequences of successive Steiner and Minkowski symmetrizations. We state an equivalence result between the convergences of those sequences for Minkowski and Steiner symmetrizations. Moreover, in the case of independent (and not necessarily identically distributed) directions, we prove the almost-sure convergence of successive symmetrizations at exponential rate for Minkowski, and at rate with c > 0 for Steiner.

Type
Stochastic Geometry and Statistical Applications
Copyright
© Applied Probability Trust 

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